# How to prove that the language { ww | w ∈ {a,b}* } is / isn't context free? [duplicate]

Is the language { ww | w ∈ {a,b}* } context free? I have tried to create a pushdown automaton but I didn't find any solution. I think you need a queue and not a stack.

Is there a way to prove this statement using the pumping lemma?

## marked as duplicate by Raphael♦Jun 9 '15 at 12:42

• @Raphael: One example might be bulk assignment such as my ($a,$b, $c) = ($c + 4, "d", \$a) in Perl. Now Perl variables aren't sufficiently strongly typed to make this a convincing example, but constructs such as this might make it attractive to support queues in your parsing automaton. – reinierpost Jun 9 '15 at 14:32